Question
I have 2 10 year old mulberry trees that have developed over the past 5 years a black colored on the trunk of the trees and also unto their branches. Some of the branches which are covered with the black thing nothing grows from it. The black stuff is not slimy or powdery. The bark of the tree does not fall off, but I notice it does have small cracks. There is no gooey stuff coming from it. The leaves are large and green. But the black stuff seems to be advancing slowly. What can it be? Please help because it seems it is on both trees!!

Answer
Cesar:
Your description sounds much like a condition called sooty mold.  This is a group of fungal organisms that grow on "honeydew", the sugary excrement of certain insects.  See the attached website that has a bulletin that I have prepared on the subject.  

http://www.uaex.edu/Other_Areas/publications/PDF/FSA-7555.pdf

If the trees are large, chemical control may not be very practical.  From what you describe, the leaves are OK, so I would not expect a significant health impact on the bark if the tree is being fertilized and watered to encourage good vigorous growth.

Regards
Steve